The present invention relates to data communications equipment, e.g., modems, and, more particularly, to the equalization of signals in a data communications system.
To varying degrees, inter-symbol interference (ISI) is always present in a data communications system. ISI is the result of the transmission characteristics of the communications channel, i.e., the "channel response," and, generally speaking, causes neighboring data symbols, in a transmission sequence, to spread out and interfere with one another. If the channel response is bad, or severe, ISI becomes a major impediment to having low error rate communications between two data endpoints. In fact, at higher data rates, i.e., frequencies, the affect of ISI is more severe since there is more high frequency attenuation in the transmission channel. Consequently, current efforts to push transmission speeds higher and higher in the local loop environment must effectively contend with ISI effects on a transmitted data signal to be successful.
As known in the art, ISI is typically removed by a decision feedback equalizer (DFE) in a receiver. There are theoretically two mathematically equivalent forms of DFEs. One is the ISI predictive DFE (ISI-DFE), the other is the noise predictive DFE (NP-DFE). Although mathematically equivalent, in practice there are limits on the performance of each, limits that become noticeable in high speed communications systems. In particular, the performance of both the ISI-DFE and the NP-DFE are affected by noise introduced from the communications channel, i.e., channel noise, and error propagation.
In the case of an ISI-DFE, there is a feedforward filter section and an ISI predictive feedback filter section, each of which removes a portion of the ISI. Unfortunately, the channel noise after processing by the feedforward filter section may appear slightly colored, not white. That is, the feedforward filter section does not necessarily converge to an ideal pre-whitening solution using a typical adaptation algorithm. This colored noise provided by the feedforward filter section causes performance degradation. In other words, the ISI-DFE performance is limited, i.e., sub-optimal.
Alternatively, as described above, a receiver may use an NP-DFE. The latter includes a linear equalizer followed by an NP feedback filter section. The linear equalizer theoretically removes all of the ISI, while the NP feedback section removes any colored channel noise. However, in the design of a linear equalizer there is a trade-off between noise enhancement and ISI compensation--this trade-off is represented by use of a "minimum mean squared error" (MMSE) criteria in the linear equalizer to remove the ISI. Consequently, the signal provided by the linear equalizer always has a residual form of ISI present. This residual form of ISI causes performance degradation so that even an NP-DFE does not provide the optimal DFE performance. It should be noted that an alternative "zero-forcing" criteria can be used in the linear equalizer to force the ISI to zero. However, this zero-forcing approach is only practical if there is no spectral null in the channel response.
Notwithstanding the above described practical limitations to the use of either an ISI-DFE or an NP-DFE, some in the art have realized there is some benefit to using a hybrid type of structure to improve DFE performance. For example, in the article "Design and Performance of an All-Digital Adaptive 2.048 MBIT/S Data Transmission System Using Noise Prediction", Graf et al. ISCAS 1989 pp. 1808-1812, the DFE includes a symbol-spaced pre-cursor only adaptive zero forcing feedforward filter followed by a least mean squares (LMS) ISI predictive filter and an LMS noise predictive filter in parallel. In this case, the use of the ISI predictive filter and the noise predictive filter compensate for the use of the symbol-spaced pre-cursor only zero forcing feedforward filter. Unfortunately, the use of the symbol-spaced pre-cursor only zero forcing feedforward filter does not provide optimal DFE performance in the presence of channel distortion and noise. Furthermore, the Graf et al. article teaches that the use of an LMS algorithm for all three filters cannot guarantee the steady-state performance. Consequently, although this hybrid type of structure is useful in this particular communications environment, it is not the complete answer to the problem of approaching optimal DFE performance in the presence of channel noise in a high speed communications system.
Further, as mentioned-above, the use of an ISI-DFE or a NP-DFE, introduces "error propagation" effects in the receiver. Both the ISI-DFE and the NP-DFE make a decision, i.e., an estimate, as to the correct data symbol. Since both the ISI-DFE and the NP-DFE utilize feedback, an incorrect estimate as to the current received symbol affects subsequent received symbols. Generally, the prior art teaches that precoding is used to remove the affects of error propagation. In the case of a receiver with an ISI-DFE, the prior art teaches that the resulting coefficient values of the ISI-DFE--as represented by the notation I(z), as known in the art--are transmitted back to the transmitter, e.g., over a reverse channel, for use by a transmitter in precoding. Similarly, in the case of a receiver with a NP-DFE, the prior art teaches that the N(z) coefficient values are transmitted back to the transmitter. Unfortunately, in the case of a hybrid DFE, the obvious combination of I(z)+N(z) does not provide the optimal solution for precoding in the transmitter.